A design method for alternating LT code degree distribution

Abstract

The present invention discloses a method for designing an alternating LT code degree distribution. The method comprises the following steps: Step 1) generating odd bits and k / R bits of an alternating degree distribution (AD) function based on a robust soliton distribution (RSD) function; Step 2) generating even bits of the alternating degree distribution function that are not k / R bits based on an improved binary exponential distribution (IBED) function; and Step 3) normalizing the alternating degree distribution function. Using this novel degree distribution for LT coding can effectively improve the error control performance of LT codes.

Description

Technical Field

[0001] The present invention belongs to the technical field of channel coding, and more particularly, relates to a method for designing alternating LT code degree distribution. Background Art

[0002] Luby Transform (LT) codes are a classic type of error control code with features such as unlimited bit rate, no need for feedback and retransmission, and low encoding and decoding complexity. They can be used as channel coding in power line communications, deep space communications, cognitive radio communications, and other fields to improve the system's anti-interference performance and reliability.

[0003] Degree distribution is a key factor in the implementation of LT code encoding and decoding. The most classic one is the Robust Soliton Distribution (RSD) formally proposed by Luby M in 2002. Although RSD has a lower decoding success rate when the redundancy is small, its degree distribution function is It can ensure that all input groups participate in the encoding process, and the number of coding groups with a degree of 1 in the decoding process remains almost constant. As long as there is no large fluctuation, the decoding process is guaranteed to continue to the end, so that all the original data can be decoded.

[0004] Compared to RSD, the Improved Binary Exponential Distribution (IBED), proposed in 2017, generates a sufficient number of degree-1 code blocks in the initial decoding phase to reduce the probability of decoding failures, resulting in an initial decoding success rate exceeding 90%. However, as decoding overhead increases, the number of degree-1 code blocks may decrease or even disappear in the later stages of decoding, leading to decoding interruptions and, consequently, weaker decoding performance than RSD.

[0005] Therefore, directly applying both to power line communication, deep space communication, cognitive radio communication and other systems using LT code as channel coding is difficult to provide good error control performance and cannot meet the system's anti-interference performance and reliability requirements. Summary of the Invention

[0006] To address the above technical problems, the present invention proposes a design method for an alternating LT code degree distribution (AD). This method utilizes the characteristics of IBED (high decoding success rate when redundancy is small) and RSD (better decoding performance when redundancy is increased) to organically combine the two to generate a new degree distribution, which can effectively improve communication reliability.

[0007] The present invention adopts the following technical solutions:

[0008] A method for designing an alternating LT code degree distribution comprises the following steps:

[0009] Step 1) Generate the odd-digit sum of AD function based on RSD function k / R Bit;

[0010] Step 2) Generate the even digits of AD function based on IBED function and it is not k / R Bit;

[0011] Step 3) Normalize the AD function.

[0012] In the above scheme, the odd-numbered sum of the AD function is generated based on the RSD function in step 1). k / R Specifically, the following steps are included:

[0013] Step 1-1), generate the RSD function expression ( ):

[0014]

[0015] in

[0016]

[0017]

[0018] In the formula, the number of coding groups with a degree of 1 is expected to remain constant during the decoding process. , is the number of input groups, is a positive constant, is the allowed probability of decoding failure, is the degree of each coding group, is the ideal soliton distribution (ISD).

[0019] Step 1-2), extract the odd bits and the sum of the RSD function k / R bits, odd bits and AD functions k / R bits. The expression is as follows:

[0020] (1)

[0021] In the above solution, step 2) generates the even-numbered bits of the AD function based on the IBED function, specifically including the following steps:

[0022] Step 2-1), generate IBED function expression ( ):

[0023]

[0024] in,

[0025]

[0026] Where, is the degree of each coding group, Enter the number of groups.

[0027] Step 2-2), extract the even digits of the IBED function and not k / R Bit, as the even bit of AD function. The expression is as follows:

[0028] (2)

[0029] In the above scheme, the AD function is normalized in step 3) and the expression is as follows:

[0030] (3)

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] This invention leverages the high decoding success rate of IBED when redundancy is low and the improved decoding performance of RSD when redundancy is increased. By organically combining the two, it generates an alternating LT code degree distribution. Using this novel degree distribution for LT coding can effectively improve the error control performance of LT codes. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a schematic diagram of the principle of the alternating LT code degree distribution design method provided by the present invention.

[0034] Figure 2 yes When , the performance of the present invention, RSD degree distribution and IBED degree distribution are compared. DETAILED DESCRIPTION

[0035] The preferred embodiments are described in detail below in conjunction with the accompanying drawings. It should be emphasized that the following description is merely exemplary and is not intended to limit the scope of the present invention and its application.

[0036] See Figure 1 The present invention provides a method for designing an alternating LT code degree distribution, comprising the following steps:

[0037] Step 1), generate the RSD function expression ( ):

[0038]

[0039] in

[0040]

[0041]

[0042] In the formula, the number of coding groups with a degree of 1 is expected to remain constant during the decoding process. , is the number of input groups, is a positive constant, is the allowed probability of decoding failure, is the degree of each coding group, is the ideal soliton degree distribution (ISD).

[0043] Step 2), extract the odd bits and the sum of the RSD function k / R bits, odd bits and AD functions k / R bits. The expression is as follows:

[0044] (1)

[0045] Step 3), generate IBED function expression ( ):

[0046]

[0047] in,

[0048]

[0049] Where, is the degree of each coding group, Enter the number of groups.

[0050] Step 4) Extract the even digits of the IBED function and use them as the even digits of the AD function. The expression is as follows:

[0051] (2)

[0052] Step 5) Normalize the AD function. The expression is as follows:

[0053] (3)

[0054] Specifically, in the present invention, , using AD degree distribution to perform 1000 LT encoding and decoding. Take this as an example to illustrate,

[0055] Step 1), generate Degree distribution, including the following steps:

[0056] Step 1-1), generate the RSD function expression ( ):

[0057]

[0058] in

[0059]

[0060]

[0061] In the formula, the number of coding groups with a degree of 1 is expected to remain constant during the decoding process. , is the number of input groups, is a positive constant, is the allowed probability of decoding failure, is the degree of each coding group, is the ideal soliton degree distribution (ISD).

[0062] Step 1-2), extract the odd bits and the sum of the RSD function k / R bits, odd bits and AD functions k / R bits. The expression is as follows:

[0063] (1)

[0064] Steps 1-3), generate IBED function expression ( ):

[0065]

[0066] in,

[0067]

[0068] Where, is the degree of each coding group, Enter the number of groups.

[0069] In steps 1-4), extract the even digits of the IBED function and use them as the even digits of the AD function. The expression is as follows:

[0070] (2)

[0071] Steps 1-5) Normalize the AD function, and the expression is as follows:

[0072] (3)

[0073] Step 2), divide the original data into k Input packets, each encoded packet is generated by the following steps:

[0074] Step 2-1), from The degree of a randomly selected coding group in the degree distribution d ;

[0075] Step 2-2), randomly and uniformly select d input packets as "adjacent" to the encoded packet;

[0076] Steps 2-3), this d The "adjacencies" are XORed to generate coded groups;

[0077] Repeat steps 2-1) to 2-3) to generate the coding sequence.

[0078] Step 3) uses the belief propagation (BP) decoding algorithm to perform LT decoding, including the following steps:

[0079] The receiving end receives slightly larger k The coding matrix is ​​reconstructed and then the BP algorithm is used for decoding, which includes the following steps:

[0080] Step 3-1), the degree is 1 ( d = 1) is directly copied to the input packet connected to it.

[0081] Step 3-2): The translated input group is XORed with its "adjacent" group and then replaces the original encoded group. At the same time, its connection relationship is deleted, and the degree of the encoded group is reduced by 1.

[0082] Repeat steps 3-1) and 3-2) until the decoding is completed.

[0083] Figure 2 Given when When , the performance of AD degree distribution, RSD degree distribution and IBED degree distribution is compared. Figure 2 It can be seen from the figure that when the parameters are the same, the decoding performance of LT encoding and decoding using AD degree distribution is better than that of RSD degree distribution and IBED degree distribution.

[0084] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for designing alternating LT code degree distribution, characterized in that: Including steps: Step 1), based on the robust soliton distribution RSD function generation A d Odd-digit sum of functions k / R bits, where k is the number of input packets, R is the number of code groups with the expected degree of 1 during decoding, and d is the degree of each code group; Step 2), based on the improved binary exponential distribution IBED function A d The even number of the function is not k / R Bit; Step 3) A d The function is normalized to obtain the alternating degree distribution AD function.

2. The alternating LT code degree distribution design method according to claim 1, characterized in that: The step 1) specifically includes the following steps: Step 1-1), generate RSD function expression : in In the formula, the number of coding groups with a degree of 1 is expected to remain constant during the decoding process. , is the number of input groups, is a positive constant, is the allowed probability of decoding failure, is the degree of each coding group, is the ideal soliton distribution (ISD); Step 1-2), extract the odd bits and the sum of the RSD function k / R bit, as A d Odd-digit sum of functions k / R The expression is as follows: (1)。 3. The alternating LT code degree distribution design method according to claim 1, characterized in that: The step 2) specifically includes the following steps: Step 2-1), generate IBED function expression : in, Step 2-2), extract the even bits of the IBED function as A d The even-numbered bits of the function are expressed as follows: (2)。 4. The alternating LT code degree distribution design method according to claim 1, characterized in that: The step 3) specifically includes A d The function is normalized to obtain the AD function expression : (3) in, 。

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